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Experimental and numerical investigation of the heat transfer augmentation and pressure drop in simple, dimpled and perforated dimpled louver fin banks with an in-line or staggered arrangement
Accepted Manuscript Experimental and numerical investigation of the heat transfer augmentation and pressure drop in simple, dimpled and perforated dimpled louver fin banks with an inline or staggered arrangement Farhad Sangtarash, Hossein Shokuhmand PII:
S1359-4311(15)00205-7
DOI:
10.1016/j.applthermaleng.2015.02.073
Reference:
ATE 6425
To appear in:
Applied Thermal Engineering
Received Date: 20 November 2014 Accepted Date: 25 February 2015
Please cite this article as: F. Sangtarash, H. Shokuhmand, Experimental and numerical investigation of the heat transfer augmentation and pressure drop in simple, dimpled and perforated dimpled louver fin banks with an in-line or staggered arrangement, Applied Thermal Engineering (2015), doi: 10.1016/ j.applthermaleng.2015.02.073. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Experimental and numerical investigation of the heat transfer augmentation and pressure drop in simple, dimpled and perforated dimpled louver fin banks with an in-line or staggered
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arrangement
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Farhad Sangtarash*, Hossein Shokuhmand,
Mechanical Engineering Department, University of Tehran, Tehran, Iran
*
Corresponding Author’s Contact:
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Email addresses: [email protected]; [email protected]
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Email: [email protected], Tel: (+9821)8887-5772, Fax: (+9821)88875771
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Abstract Numerical and experimental models have been developed to investigate the effect of adding an in-line and staggered arrangement of dimples and perforated dimples to multilouvered fins on the heat transfer augmentation and the pressure drop of the air flow through a
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multilouvered fin bank. Three-dimensional simulations of single row of louvers were conducted for the given geometries. Simulations were performed for different Reynolds numbers. The simulations revealed that the heat transfer and temperature augmentations
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occur due to the existence of a circulation region that is created by the dimple. Additionally, continuous temperature gradients have been observed over the louver surface with the highest
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temperature at the base of the louver and the lowest temperature at the middle of the louver. Additionally, the difference between these two points is more obvious with greater Reynolds numbers. Fin efficiency and fin effectiveness were calculated to assess louver performance. The air-side performance of the heat exchanger is evaluated by calculating the Colburn j
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factor and the Fanning friction f factor. The results demonstrate that adding dimples on the louver surface increases the j factor and the f factor. Likewise, adding perforation to the dimples results in the same increase. The present results indicate that compared with the in-
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performance.
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line arrangement, the staggered arrangement could effectively enhance the heat transfer
Keywords: Multilouvered fin, Dimple, Perforation, In-line, Staggered
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1. Introduction Compact heat exchangers have many industrial uses, such as in refrigeration, air conditioning, and automotive applications, and many attempts have been made to improve their performance. The commonly applicable way to improve the overall performance of the
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compact heat exchanger is to use interrupted surfaces on the fin side. The implementation of dimples, louvers, and perforation on fins has been shown to achieve the best enhancement of compact heat exchanger performance. Many numerical and experimental attempts have been
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performed to improve the heat transfer of compact heat exchangers using dimples and multilouvered fins. Kays and London [1] published the first reliable data on louvered fin surfaces.
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Beauvias [2] performed flow visualization experiments on a louvered fin array as the first study in this area. This work showed that louvers actually redirect the flow between the fins. Davenport [3] demonstrated two asymptotic flow regimes: duct directed flow and louver
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directed flow. Smoke trace studies were also performed on a scale model, which was ten times smaller, of a non-standard variant of a corrugated louvered fin geometry. Finally, he developed the heat transfer and friction correlations for corrugated louvered fin geometry.
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Chang and Wang [4] tested 27 samples of louvered fin heat exchangers with different geometrical parameters in an induced-draft, open wind tunnel and carried out extensive
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experiments on the heat transfer and the pressure drop characteristics of brazed aluminum heat exchangers. Rugh et al. [5] experimentally studied the use of a high fin density louvered surface in automobiles.
Some other attempts have been made to develop two-dimensional models of louvered fin surfaces. Achaichia and Cowell [6] modeled only one louver in a fully developed flow region by assuming cyclic boundary conditions. Suga et al. [7] performed a finite difference analysis on the two-dimensional flow and the heat transfer characteristics of louvered fins. Achaichia
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ACCEPTED MANUSCRIPT et al. [8] used a novel mesh structure with mesh lines running parallel to the louvers and extending over several fins. Dong et al. [9] studied the air-side heat transfer and pressure drop characteristics for 20 types of multi-louvered fin and flat tube heat exchangers. Hsieh and Jang [10] carried out a 3-D numerical analysis on the heat and fluid flow by increasing or
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decreasing the louver angle patterns.
The use of dimpled surfaces, as a type of enhanced surface, has received attention in the past decades due to their good heat transfer characteristics and low pressure drop penalties.
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Afansayev et al.[11] studied the effects of shallow dimples on flat plates on the overall heat
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transfer capacity and pressure drop. These authors reported a significant heat transfer enhancement (30- 40 %) at a low pressure drop cost. Ligrani et al. [12] experimentally investigated the flow structure in dimpled surfaces and demonstrated the existence of a flow recirculation zone in the upstream half of the dimple. Zhengyi et al. [13] observed a symmetric 3-D horseshow vortex inside a single dimple using laminar flow simulations.
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Additionally, the flow structure and the heat transfer in dimpled channels with fully turbulent regimes have been studied in the literatures [14]. Elyyan and Tafti [15] investigated the flow
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and heat transfer characteristics of dimpled multi-louvered fins. These authors reported not only significant heat transfer augmentation but also a considerable amount of friction loss
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augmentation through dimpled louvers. Additionally, their work showed that perforations on dimples have a sharp impact on heat transfer augmentation. In another numerical study [16], these same researchers introduced a novel geometry that was the result of altering the dimple shape. Greater heat transfer and fiction loss values were reported for this geometry. These researchers have also reported that the turbulence level increases due to the shear layer induced by their new geometry’s split dimples. Elyyan et al. [17] investigated the effect of the existence of dimpled fins in compact heat exchangers for heat transfer enhancement. These researcher conducted direct and large-eddy 4
ACCEPTED MANUSCRIPT simulations in a fin bank with dimples and protrusions over encompassing laminar, transitional and fully turbulent regimes. Shokuhmand and Sangtarash [18] conducted experimental and numerical studies on the heat transfer and flow efficiency of multilouvered fins. These authors reported that implementing simple and perforated dimples on the louvers
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enhance the heat transfer and flow efficiency significantly. In previous studies [19, 20], the j factor and f factor have been utilized to characterize the heat transfer and pressure drop of simple louver fin banks.
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The present study experimentally and numerically investigates the effect of fin geometry,
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which includes the simple louver, the in-line and staggered dimpled louver, and the in-line and staggered dimple-perforated louver, on the heat transfer in multilouvered heat exchangers. To the best of our knowledge, no similar attempts have been carried out using the temperature distribution of fin surface to calculate the heat transfer. The temperature distribution over the louver surface is simulated for five independent geometries. The
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computational results are compared with data obtained from experiments. The fin efficiency and fin effectiveness are introduced to evaluate the performance of the fin geometry on heat
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transfer. Finally, the j factor and f factor are computed to investigate the variation of heat
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transfer and pressure drop as function of the Reynolds number for different fin geometries.
2. Experimental
A low turbulence wind tunnel, Model No.TE.44/D Manufactured by PLINT and PARTNERS ENGINEERS LTD, was used in this research. The cross section of the measurement section is 460 x 460 mm and the length of the test section is 600 mm. The non-uniformity of the velocity distribution is negligible. The turbulence intensity is less than 0.2 for the largest Reynolds numbers in our test domain. The experiment apparatus is shown in Figure 1.
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Figure 1. Experimental apparatus (a) external view (b) internal view
The fin array geometry used in these calculations consists of an entrance and exit louver with four louvers on either side of the redirection louver. A scaled-up (ratio of 10) inclined louvered fin model of an automobile radiator was used as simple model without dimples and perforations. Additionally, four samples, including an in-line and staggered arrangement with dimples and perforated dimples, were constructed to have the same size. The five geometries that were studied in this research are listed in Table 1.
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Characteristic Simple louver Louver with simple dimple arrangement Louver with simple perforated dimple arrangement Louver with staggered dimple arrangement Louver with staggered perforated dimple arrangement
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Case 1 2 3 4 5
DeJong and Jacobi [19] presented a computational method to determine the minimum required rows of fins for flow visualization studies without losing periodic flow. This method
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is used in this research. Figure 2 shows the schematic structure of the three types of
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experimental apparatus with their geometrical parameters. For all the calculations in this
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article, the louver thickness is fixed at 1 mm. Further geometrical details are listed in Table 2.
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Figure 2. Schematic structure of the multilouvered heat exchanger (a) simple multilouvered fin array (b) an individual dimpled louver (c) perforated dimpled louver layout (d) perforated dimpled louver with staggered arrangement
Table 2. List of geometrical parameters
Case Simple Louver Dimpled Louver Perforated Louver
Fp* 10.0 mm 10.0 mm 10.0 mm
Lp* 10.0 mm 10.0 mm 10.0 mm
S1 * 8.0 mm 8.0 mm 8.0 mm
θ 30° 30° 30°
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S2 * 10.0 mm 10.0 mm 10.0 mm
S3 * 10.0 mm 10.0 mm 10.0 mm
r
d
-
-
6.0 mm 6.0 mm
2.5 mm
ACCEPTED MANUSCRIPT A temperature controller circuit was designed to maintain the temperature at 100°C to maintain a constant temperature condition at both sides of each louver. The controller will verify the temperature 20 times per second to achieve a minimum deviation from the setpoint. An energy meter was used to verify that energy that is consumed to set the temperature of
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both sides of each louver to the setpoint value. A data gathering system was designed to make online measurement of the temperature and the pressure. The temperatures from seven zones on the surface of different louvers have been measured using thermal sensors to determine the
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Reynolds numbers. The positions of the measurement zones are shown in Figure 3. All values were recorded when the temperature of the measurement zone stabilized. Additionally, the
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pressures upstream and downstream of each louver were measured to calculate the pressure
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drop.
Figure 3. Positions of the measurement zones (a) top view (b) side view
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ACCEPTED MANUSCRIPT 3. Theory 3.1. Mathematical theory The governing equations for momentum and energy conservation are solved in a general
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boundary conforming coordinate system. Periodic boundary conditions are applied in the transverse direction to include the thermal wake effects between successive rows of fins. A Dirichlet boundary condition is applied velocity and temperature fields at the entrance of the
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array.
The governing equations can be recast into dimensionless forms using a characteristic length,
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the louver pitch LP*, a characteristic velocity, the fin array inlet velocity uin* and a * * temperature scale given by (T f − Tin ) , where Tf* is the average temperature of the louver
surface. No slip and no penetration conditions for the velocity field and a no temperature jump condition for temperature field are applied on the louvers surfaces. The non-
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* * dimensionalization would result in a Reynolds number defined by Re = Rein = uin Lp /ν and
Dirichlet boundary condition u in = 1 and Tin = 0 at the entrance of the array. The Prandtl
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number is fixed at 0.7 for air. Patrick and Tafti [21] suggested that LES method can be used to study low Reynolds turbulent flows in multilouvered geometries. DeJong and Jacobi [19]
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suggested that for a similar multilouvered array layout the flow is steady and laminar for low Reynolds numbers. Flow with higher Reynolds leads to larger vortices and will be converted from laminar to transitional and turbulent regimes. The dimensional heat flux on the louver surface is defined as
q '* = − k *
∂T * = h * (T f* − Tref* ) * ∂n
(1)
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reference temperature. Using the non-dimensionalized variables the above equation is expressed as
k* * ∂T (T f − Tin* ) = h* (T f* − Tin* )(1 − Tref ) * Lp ∂n
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q'* = −
(2)
The non-dimensional heat flux and Nusselt number can be define as:
Nu =
* f
h* L*p k*
* in
=−
∂T ∂n
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k (T − T ) *
(3)
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q' =
q '* L*p
∂T ∂n = (1 − Tref ) −
(4)
Tout − Tin 1 − Tin ln( ) 1 − Tout
(5)
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Tref = 1 −
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In this article Tref is calculated by the log-mean temperature equation:
For each louver, Tref is calculated using each computational input and output data. Tin and
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Tout are averaged on the upstream and downstream boundary of each louver, respectively. To assess the effectiveness of the multilouvered heat exchanger, we introduce fin efficiency and fin effectiveness. Fin efficiency is the ratio of heat transfer from the actual fin to the heat transfer of an imaginary fin of the same geometry and same conditions but with a temperature equal to that of the fin base. (T f* − Tref* ) q '* η= * = * q 'max (Tb − Tref* )
(6)
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ACCEPTED MANUSCRIPT where Tb* is the temperature of the fin base. Additionally, fin effectiveness is the ratio of heat transfer from the fin to the heat transfer if the fin did not exist. In other words, this quantity explains how much extra heat is being
ε=
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transferred by the fin. q* h * A finbase (Tb* − Tref* )
(7)
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where Afinbase is the base surface of the fin. The base surface of the fin is intersection of the louver and the tube wall and it is defined as louver thickness × louver width which is o.12,
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0.18, and 0.1 cm2 for entrance/end louver, redirection louver, and the inclined louvers, respectively.
In this section, we characterize the heat transfer by defining the Colburn j factor and the
j=
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pressure drop by the f (friction) factor. The Colburn j factor is defined as 2 h* Pr 3 * C p ρU
(8)
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where Cp, Pr and ρ are the constant heat capacity, Prandtl-number, and density of the air, respectively. U* is the mean velocity through the minimum flow area. h* can be defined in
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terms of the total heat transfer rate (Q*) and the logarithmic mean temperature difference LMTD.
Q* h = (∑ A fin ,i )LMTD *
(9)
and
LMTD =
∆To* − ∆Ti* ln(∆To* / ∆Ti* )
(10) 12
ACCEPTED MANUSCRIPT * Here, ∆Ti * = T f*, entrance − Tin* and ∆To* = T f*,end − Tout .
The friction f factor is defined as: ∆P * 2 A fin ρU * 2 Ac
*
2
2
(kc + ke + k w )
n 2 ) 16
(12)
(13)
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kw = (
ρU *
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∆P = ∆Pt − *
(11)
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f =
where ∆Pt* and ∆P* are the total and frictional pressure drop through louver fin bank, Afin is the total surface of fin, and Ac is the minimum flow area. The parameter n stands for number
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of louver regions, kc and ke are the coefficients for pressure loss at the inlet and outlet of the fin bank, and kw is the influence factor of the louver regions. According to the geometry parameters of the condenser and the graph given by Kay and London [1], the kc is 0.4, 0.45,
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and 0.43 for the simple louver, dimpled louver, and perforated dimpled louver, respectively and ke is 0.2, 0.23, and 0.21 for the simple louver, dimpled louver, and perforated dimpled
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louver, respectively.
For comparison between the numerical and experimental data, the mean relative deviation (MRD) is defined as
1 MRD = N
x iexp − x icalc ∑ x exp i
(14)
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3.2. Computational details The momentum and energy equations were solved using second-order central-difference discretization. The commercial package Fluent 6.3 [22] was used to simulate the
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computational three-dimensional models. As mentioned previously, five geometries have been modeled to obtain the results for the CFD predictions. We have studied low and medium
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Reynolds number regimes (Re = 100 to 1200) using large eddy simulation (LES) methods. The inlet velocities lie in the range of 0.16 m/s to 1.92 m/s for this Reynolds number domain. Previous studies [16, 21] have explained that the LES method is more capable for complex geometrical configurations. A suitable grid of 2,151,382 points was adopted to obtain the
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most accurate results while being less time consuming for convergence. One half of the fin height has been modeled for the numerical calculations, and the results for the other half are gained by specifying a symmetric boundary condition along the middle surface of the entire
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domain. The inlet velocity upstream and the outflow velocity downstream of the louvers have been set as boundary conditions. The constant temperature boundary condition has been
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imposed on the wall at the base of the louvers. The properties of the air as the fluid and copper as the louver material have been listed in Table 3 at temperature 25°C which is the set room temperature for both experimental and simulation condition. Since, the air properties change with the temperature increases, property changes due to the temperature increase, has been taken into account in the simulation process.
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ACCEPTED MANUSCRIPT Table 3. Properties of air and copper at the room temperature (25°°C)
Specific Heat Capacity (J.kg-1.K-1) 1006.43 385
Thermal Conductivity (W.m-1. K-1) 0.024 401
Viscosity (kg.m-1.s-1) 1.789×10-5 -
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Density (kg.m-3) Air 1.225 Copper 8920
4. Simulation Accuracy Verification
To begin discussing the results of the various geometries we must first verify the accuracy of
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the model with one existing set of data. Here, we used the report by Zhang and Tafti [14] on
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simple multilouvered geometry.
Figure 4. Comparison of non-dimensional heat flux distribution
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Figure 4 presents the non-dimensional heat flux distribution through louvers based on data from Zhang and Tafti [14] and the presented model for Case 1 with Re = 1000. The data sets are observed to be approximately the same (less than 5% deviation).
5. Results and Discussion In this work, the effect of louver geometry on the heat transfer was investigated. Three typical geometries, which included simple, in-line dimple and perforated dimple louvers, were evaluated with respect to their heat transfer properties. Additionally, a staggered 15
ACCEPTED MANUSCRIPT arrangement of dimples and perforated dimples were taken into account as a new structure to enhance the performance of the heat exchanger. In contrast to previous studies [14, 18], the distribution of the temperature through louvers were not neglected. The middle row of the louvers array as selected for evaluation and comparison of the results obtained from the
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experimental and numerical study. Figure 5 shows the contour of the temperature distribution for five cases with Re = 600. As shown in Figure 5, in each louver the temperature decreases as the distance from the louver base increases. Additionally, the temperatures of the louvers
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increased in the direction of the fluid flow. This trend is consistent because the heat is transferred from the heat exchanger to the fluid, the fluid becomes warmer in the direction of
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flow, and the difference between the temperature of fluid and louvers decreases. Figure 6 shows that the implementation of perforations on the dimples removed trap zones and increased the flow efficiency. This effect increased the heat flux, which transferred more heat from the heat exchanger to fluid flow. The staggered arrangement of dimples and perforated
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banks.
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dimples makes the flow more turbulent to enhance the performance of multilouvered fin
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(b)
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Figure 5. a) Temperature (K) contours on five cases in Re = 600 b) Louver boundary condition
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Figure 6. Vector velocity of fluid surrounding (a) simple dimple (b) perforated dimple in Re = 600
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The temperatures of the measured zones, which are shown in Figure 3, were determined numerically for five cases with Re = 1200 and were compared with the recorded value from
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the experimental apparatus in Figure 7. The results show that the calculated temperatures are in good agreement with the experimental values. Comparison of the measured temperature
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from five cases shows the smallest value is a staggered arrangement with a dimpled and perforated louver (Case 5). This result is because this arrangement makes the flow more turbulent, increases the heat transfer rate, and causes the temperature of louver surfaces decrease faster than other geometries.
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Figure 7. The temperature of louver surfaces
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Figure 8 plots the variation of the non-dimensional heat flow (q) on a louver-by-louver basis for the five different cases. As shown in Figure 8, the heat flow from first louver is greater than the last louver, and the value of the heat flow decreases downstream. Because the surface of louver 6 is greater than the other louvers, the heat flow increases at louver 6 and
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then continues its decreasing trend. It can be concluded by comparing Figures 8 (a) and (b) that the heat flow is increasing with Re number increase. In all five cases, the variation in the range of the heat flow for Re = 1200 was greater than for Re = 600. The heat flow was
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increased by adding dimples to the louver surfaces, and this value became greater in the case of perforated dimples. Additionally, the heat flow in the case of the staggered arrangement
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was greater than in the in-line arrangement. The addition of perforated dimples and applying a staggered arrangement increased the heat flow by up to 6.4% and 9.9% compared with the simple louver for Re numbers of 600 and 1200, respectively.
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Figure 8. Distribution of non-dimensional heat flow for (a) Re = 600 and for (b) Re = 1200
Figure 9 shows the total heat transfer energy ratio for the in-line dimple, the in-line dimpleperforation, the staggered dimple, and the staggered dimple-perforation samples compared with the simple louver case. These measurements were obtained using the energy meter from the experimental apparatus at different Reynolds numbers.
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Figure 9. Total heat transfer ratio compared with the simple louver case
Figure 9 shows that the total heat transfer for cases 2 through 5, which has been measured during the experiment, are nearly the same for low Reynolds numbers, but the heat transfer changes for higher Reynolds numbers.
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The Nusselt number variation on a louver-by-louver basis is shown in Figure 10. In Case 5, the average Nu numbers for louvers are primarily greater than the Nu numbers for the simple louver case. It can be concluded from Figure 10 that unsteady flow oscillations and vortex
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shedding in the downstream half of the array causes the mean heat transfer coefficient to be
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greater in the downstream half of the fin array; this is especially true for Case 5.
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Figure 10. Distribution of the Nusselt number for (a) Re = 600 and for (b) Re = 1200
The maximum heat transfer occurs where the maximum temperature difference exists. Therefore, the ideal heat transfer situation for louvered fins would exist if the temperature of the entire louver surface was the same as the wall temperature. Due to both the louver’s thermal resistance and the heat energy dissipated by flow, the temperature of louver surface is less than its base. Because dimples increase the heat transfer surface and heat transfer rate, the temperature difference between the middle regions of the dimpled louvers and the fluid flow become smaller. 22
ACCEPTED MANUSCRIPT The implementation of the dimples in different types increases the heat transfer surface by about 14% for cases 2 and 4 and 11.5% for cases 3 and 5. While, applying the dimples causes the increase of the heat transfer by different percentages for different cases. For instance, for Re number of 1200, the total heat transfer is 6.5%, 8.9%, 9.1%, and 9.9%
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greater than the simple louver geometry for cases 2, 3, 4, and 5, respectively. If we increase the heat transfer surface 14% more with the increase of the length of the simple louver instead of adding the dimples, the total heat transfer increases by about 4.5% which is less
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than all other cases mentioned above.
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The fin efficiency and fin effectiveness have been introduced to characterize the effect of implementing dimples and applying a staggered arrangement on the multilouvered heat exchanger performance. The fin efficiency and fin effectiveness for all cases with Re = 1200 have been shown in Figure 11. Figure 11(a) shows that the fin efficiency for Case 1 is greater than other geometries, which was expected given Eq. 6 because the average temperature of
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the louvers in this case is close to the base temperature. Likewise, the greater amount of heat transfer in Case 5 reduces the temperature of the louver surfaces and makes the fin efficiency
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less than the other cases.
Figure 11(b) shows the fin effectiveness values for Case 5 is greater compared with the other
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cases in the upstream half of the fin array and, in the downstream half of the fin array, the effectiveness value decreases. It can be concluded that the first louvers are more effective in transferring heat and the maximum amount of heat is transferred in these louvers. The fin effectiveness values for Case 1 through Case 5 when enhancing the performance of heat exchanger are 316%, 335%, 340%, 341%, and 344% for Re = 1200, respectively.
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Figure 11. (a) Fin efficiency and (b) fin effectiveness for all five cases with Re = 1200.
Heat transfer and pressure drop characteristics are presented in terms of non-dimensional
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parameters: the j factor and the f factor. Figure 12(a) shows the value of the j factor for all cases for different Reynolds numbers using logarithmic scales as well as the results of the simple louver of Xiaogang and Tafti [23]. It can be observed from Figure 12(a) that the value of the j factor decreases when the Reynolds number increases. Figure 12(a) also shows that implementing dimples lead to increasing the value of the j factor over the louvers. Furthermore, perforated dimples show better j factor values than the simple and dimpled louvers. Additionally, the staggered arrangement makes the flow more turbulent and causes
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ACCEPTED MANUSCRIPT greater j factor values. This geometry increases the j factor for all Re numbers 54% more compared with the simple louver geometry on average. The MRD value for cases 1 through 5 is 7.5%, 5.4%, 5.7%, 5.2%, and 7.5%, respectively.
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Figure 12(b) shows the value of the f factor for the five cases with Reynolds numbers from 100 to 1200 using logarithmic scales as well as the results of the simple louver of Xiaogang and Tafti [23]. It can be observed that the f factor decreases as the Reynolds number increases for all cases. Figure 12(b) also illustrates that, for the same Reynolds number, the dimpled
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louver results in a greater f factor value. This larger f factor is obviously because of the effect
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of the larger pressure drop caused by the dimples. Additionally, as expected, the f factor for the staggered arrangement is greater than the in-line arrangement. Case 4 and Case 5 increase the f factor by 43% and 49% on average, respectively, whereas Case 2 and Case 3 increase the f factor value by 31% and 40% more than Case 1, respectively. The MRD value for cases 1 through 5 is 6.6%, 5.1%, 5.4%, 6.5%, and 6%, respectively. It can be seen from Figure 12
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that the results of the simple louver case of the present work are in good agreement with the results of Xiaogang and Tafti [23].
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According to Figures 12a and 12b, one can observe a deviation from linearity at about Re=400 which may be attributed to the transition between laminar and turbulent regimes. It is
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noteworthy that this nonlinearity occurs in lower amount of Reynolds number in dimple and perforation cases specially in case 5 which confirm dimples and perforations particularly in staggered arrangement make the flow more turbulent. Besides, it causes higher heat transfer and pressure drop rates.
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Figure 12. (a) j factor and (b) f factor for all cases with Re = 100 through 1200 using logarithmic scales.
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Factor j/f (1/3) [24] is adopted to evaluate the overall thermal hydraulic performance and the enhanced heat transfer effect of the louver region fins. The larger factor j/f (1/3) is, the better the enhanced heat transfer effect will be. Plots of j/f (1/3) factor versus Re number for different cases are presented in Figure 13. It can be seen from Figure 13 that the j/f (1/3) factor curve in the case of staggered perforated dimpled louvers (case 5) is the highest one with respect to the other types of louvers, which can be attributed to the fact that the overall thermal performance of the case 5 is greater than the other types.
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ACCEPTED MANUSCRIPT The values of j/f (1/3) factor increased by about 23%, 28%, 29%, and 40% compared with the simple louver geometry for the cases 2, 3, 4, and 5 respectively, which indicates that the modified louvers particularly staggered perforated dimpled arrangement provided higher
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performance for heat transfer with respect to the simple louver.
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Figure 13. Plots of j/f (1/3) factor versus Re number for different cases.
6. Uncertainty Analysis
Uncertainty of each experimental result is one of the most important factors which make the
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results to be more comprehensive. These uncertainties are affected by inevitable errors
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occurring in the experimental measurements which can be interpreted to the uncertainty of individual measuring instruments. Based on the uncertainty analysis method of Kline and McClintock [25], propagation of uncertainty in the final result is affected by the uncertainties of independent variables. This method is employed to estimate the uncertainties of experimental results. The maximum uncertainties of Nusselt number, j factor, and f factor are calculated and the results are shown in Table 4.
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ACCEPTED MANUSCRIPT It can be concluded from this research work that the calculated values of Nusselt number, j factor, and f factor cover a range of possible values based on the uncertainties presented in Table 4. In addition, it should be noted that all the experiments have been repeated three
Table 4. Maximum value of uncertainties for different variables
Nusselt number ±2.4
j factor ±6.3
f factor ±5.7
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Variable Maximum value of uncertainty (%)
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times in order to have a more reliable result and to be assured of the reproducibility.
7. Conclusions
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A wide range of numerical and experimental evaluations were performed for five cases: simple louver fin bank, dimpled louver fin bank with in-line and staggered arrangement and dimpled and perforated fin bank with in-line and staggered arrangement. These experiments were performed to determine of heat transfer and pressure drop characteristics. Both the
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numerical and the experimental results show that the dimple-perforation sets with staggered arrangement had the maximum heat flux, and the total heat transfer rate increased, which was especially noticeable in larger Reynolds numbers. Experimental data showed that applying
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this geometry enhanced the heat transfer rate up to 7%, 8.2%, and 9.9% with Reynolds
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numbers of 800, 1000, and 1200, respectively, compared with the simple louver geometry. The temperature distributions through the louvers body have been calculated using numerical methods for the five cases. The simulation results are compared with the experimental data and are found to be in good agreement. The effect of dimple implementation and the application of a staggered arrangement have been evaluated using two parameters: the fin efficiency and the fin effectiveness. The results showed that dimple-perforation with a staggered arrangement had the lowest fin efficiency value but the fin effectiveness of this geometry was greater than other cases. Both j factor and the f factor for the case of dimple-
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ACCEPTED MANUSCRIPT perforation with staggered arrangement are greater compared with other geometries. Moreover, Factor j/f The values of j/f
(1/3)
(1/3)
is adopted to evaluate the overall thermal hydraulic performance.
factor increased by about 23%, 28%, 29%, and 40% in average
compared with the simple louver geometry for the cases 2, 3, 4, and 5 respectively, which
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indicates that the modified louvers particularly staggered perforated dimpled arrangement
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provided higher performance for heat transfer with respect to the simple louver.
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8. Nomenclature
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T* Tb Tf Tin Tout Tref uin* U Greek Symbols ɛ ƞ θ ν ρ Superscripts * Subscripts f, fin, louver
area, (mm2) Minimum flow area, (mm2) fin surface, (mm2) base surface of the fin, specific heat capacity, (J.kg-1.K-1) hole size, (mm) friction f factor fin pitch, (mm) heat transfer coefficient, (W.m-2. K-1) Colburn j factor thermal conductivity, (W.m-1. K-1) abrupt contraction pressure loss coefficient abrupt expansion pressure loss coefficient louver regions pressure loss coefficient dimensional louver pitch (characteristic length scale), (mm) number of louver regions number of the experimental data Nusselt number frictional pressure drop, (Pa) total pressure drop, (Pa) Prandtl number non-dimensional heat flow non-dimensional heat flux total heat transfer, (W) dimple radius, (mm) Reynolds number non-dimensional entrance / exit, redirection and inclined louver dimensions temperature, (K) non-dimensional temperature of the fin base non-dimensional fin temperature non-dimensional inlet flow temperature non-dimensional outlet flow temperature non-dimensional flow reference temperature dimensional inlet velocity (characteristic velocity scale), (m.s-1) non-dimensional mean velocity through the minimum flow area
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A Ac Afin Afinbase Cp d f Fp* h* j k* kc ke kw L p* n N Nu ∆P* ∆Pt* Pr q q' Q* r Re S1, S2 , S3
fin effectiveness fin efficiency louver angle, degree kinematic viscosity, (kg.m-1.s-1) density, (kg.m-3) dimensional quantities based on fin 30
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based on inlet based on outlet based on reference value
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in out ref
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References
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[1] W. Kays, A. London, Heat transfer and flow friction characteristics of some compact heat exchanger surfaces, Trans. ASME, 72 (1950) 1075-1097. [2] F. Beauvais, An aerodynamic look at automotive radiators, SAE Technical Paper, 1965. [3] C. Davenport, Correlation for heat transfer and flow friction characteristics of louvered fin, AIChE Symposium series, 1983, pp. 19-27. [4] Y.J. Chang, C.C. Wang, Air Side Performance of Brazed Aluminum Heat Exchangers, 3 (1996) 15-28. [5] J. Rugh, J. Pearson, S. Ramadhyani, Study of a very compact heat exchanger used for passenger compartment heating in automobiles, 28th National Heat Transfer Conference and Exhibition, 1992, pp. 15-24. [6] A. Achaichia, T.A. Cowell, Heat transfer and pressure drop characteristics of flat tube and louvered plate fin surfaces, Experimental Thermal and Fluid Science, 1 (1988) 147-157. [7] K. Suga, H. Aoki, T. Shinagawa, Numerical Analysis on Two-Dimensional Flow and Heat Transfer of Louvered Fins Using Overlaid Grids, JSME Int. J. Ser. II 33 (1990) 122-127. [8] A. Achaichia, M. Heikal, Y. Sulaiman, T. Cowell, Numerical investigation of flow and friction in louvered fin arrays, in: Proc. of the Tenth International Heat Transfer Conf. 4, Brighton, 1994, pp. 333-333. [9] J. Dong, J. Chen, Z. Chen, W. Zhang, Y. Zhou, Heat transfer and pressure drop correlations for the multi-louvered fin compact heat exchangers, Energy Conversion and Management, 48 (2007) 15061515. [10] C.-T. Hsieh, J.-Y. Jang, 3-D thermal-hydraulic analysis for louver fin heat exchangers with variable louver angle, Applied Thermal Engineering, 26 (2006) 1629-1639. [11] V.N. Afanasyev, Y.P. Chudnovsky, A.I. Leontiev, P.S. Roganov, Turbulent flow friction and heat transfer characteristics for spherical cavities on a flat plate, Experimental Thermal and Fluid Science, 7 (1993) 1-8. [12] P.M. Ligrani, N.K. Burgess, S.Y. Won, Nusselt Numbers and Flow Structure on and Above a Shallow Dimpled Surface Within a Channel Including Effects of Inlet Turbulence Intensity Level, Journal of Turbomachinery, 127 (2004) 321-330. [13] W. Zhengyi, Y. Khoon Seng, K. Boo Cheong, Numerical Simulation of Laminar Channel Flow over Dimpled Surface, 16th AIAA Computational Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics, 2003. [14] X. Zhang, D.K. Tafti, Classification and effects of thermal wakes on heat transfer in multilouvered fins, International Journal of Heat and Mass Transfer, 44 (2001) 2461-2473. [15] M.A. Elyyan, D.K. Tafti, Flow and Heat Transfer Characteristics of Dimpled Multilouvered Fins, 16 (2009) 43-60.. [16] M.A. Elyyan, D.K. Tafti, A novel split-dimple interrupted fin configuration for heat transfer augmentation, International Journal of Heat and Mass Transfer, 52 (2009) 1561-1572. [17] M.A. Elyyan, A. Rozati, D.K. Tafti, Investigation of dimpled fins for heat transfer enhancement in compact heat exchangers, International Journal of Heat and Mass Transfer, 51 (2008) 2950-2966. [18] H. Shokuhmand, F. Sangtarash, P. Student, The effect of dimple and perforations on Flow Efficiency and heat transfer enhancement in Multi louvered Fin banks, Life Science Journal, 10 (2013). [19] N.C. DeJong, A.M. Jacobi, Localized flow and heat transfer interactions in louvered-fin arrays, International Journal of Heat and Mass Transfer, 46 (2003) 443-455. [20] W. Li, X. Wang, Heat transfer and pressure drop correlations for compact heat exchangers with multi-region louver fins, International Journal of Heat and Mass Transfer, 53 (2010) 2955-2962. [21] W.V. Patrick, D.K. Tafti, Computations of flow structure and heat transfer in a dimpled channel at low to moderate Reynolds number, ASME 2004 Heat Transfer/Fluids Engineering Summer Conference, American Society of Mechanical Engineers, 2004, pp. 401-412. [22] FLUENT, User’s Guide, Release 6.3, Fluent Inc., Lebanon, New Hampshire.
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[23] Z. Xiaogang, D. Tafti, Effect of Fin Pitch on Flow and Heat Transfer in Multilouvered Fins, in, Air Conditioning and Refrigeration Center. College of Engineering. University of Illinois at UrbanaChampaign., 1999. [24] J.H. Kim, J.H. Yun, C.S. Lee, Heat-Transfer and Friction Characteristics for the Louver-Fin Heat Exchanger, Journal of Thermophysics and Heat Transfer, 18 (2004) 58-64. [25] S.J. Kline, F. McClintock, Describing uncertainties in single-sample experiments, Mechanical engineering, 75 (1953) 3-8.
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Table captions Table 1. List of fin geometries Table 2. List of geometrical parameters
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Table 4. Maximum value of uncertainties for different variables
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Table 3. Properties of air and copper at the room temperature (25°C)
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Figure captions Figure 1. Experimental apparatus (a) external view (b) internal view. Figure 2. Schematic structure of the multilouvered heat exchanger (a) simple multilouvered
dimpled louver with staggered arrangement.
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fin array (b) an individual dimpled louver (c) perforated dimpled louver layout (d) perforated
Figure 3. Positions of the measurement zones (a) top view (b) side view.
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Figure 4. Comparison of non-dimensional heat flux distribution.
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Figure 5. Temperature (K) contours on five cases in Re = 600 b) Louver boundary condition. Figure 6. Vector velocity of fluid surrounding (a) simple dimple (b) perforated dimple in Re = 600.
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Figure 7. The temperature of louver surfaces.
Figure 8. Distribution of non-dimensional heat flow for (a) Re = 600 and for (b) Re = 1200.
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Figure 9. Total heat transfer ratio compared with the simple louver case. Figure 10. Distribution of the Nusselt number for (a) Re = 600 and for (b) Re = 1200.
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Figure 11. (a) Fin efficiency and (b) fin effectiveness for all five cases with Re = 1200. Figure 12. (a) j factor and (b) f factor for all cases with Re = 100 through 1200 using logarithmic scales.
Figure 13. Plots of j/f (1/3) factor versus Re number for different cases.
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Highlights An inclined louvered fin bank has been investigated experimentally and numerically.
•
Effect of dimples and perforations in different arrangements has been investigated.
•
Temperature distribution through louvers and pressure drop have been evaluated.
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The maximum j an f factor occurs in Staggered Perforated dimple arrangement.
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Staggered perforated dimple louver shows the best thermal hydraulic performance.
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•
S1359-4311(15)00205-7
DOI:
10.1016/j.applthermaleng.2015.02.073
Reference:
ATE 6425
To appear in:
Applied Thermal Engineering
Received Date: 20 November 2014 Accepted Date: 25 February 2015
Please cite this article as: F. Sangtarash, H. Shokuhmand, Experimental and numerical investigation of the heat transfer augmentation and pressure drop in simple, dimpled and perforated dimpled louver fin banks with an in-line or staggered arrangement, Applied Thermal Engineering (2015), doi: 10.1016/ j.applthermaleng.2015.02.073. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Experimental and numerical investigation of the heat transfer augmentation and pressure drop in simple, dimpled and perforated dimpled louver fin banks with an in-line or staggered
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arrangement
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Farhad Sangtarash*, Hossein Shokuhmand,
Mechanical Engineering Department, University of Tehran, Tehran, Iran
*
Corresponding Author’s Contact:
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Email addresses: [email protected]; [email protected]
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Email: [email protected], Tel: (+9821)8887-5772, Fax: (+9821)88875771
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Abstract Numerical and experimental models have been developed to investigate the effect of adding an in-line and staggered arrangement of dimples and perforated dimples to multilouvered fins on the heat transfer augmentation and the pressure drop of the air flow through a
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multilouvered fin bank. Three-dimensional simulations of single row of louvers were conducted for the given geometries. Simulations were performed for different Reynolds numbers. The simulations revealed that the heat transfer and temperature augmentations
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occur due to the existence of a circulation region that is created by the dimple. Additionally, continuous temperature gradients have been observed over the louver surface with the highest
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temperature at the base of the louver and the lowest temperature at the middle of the louver. Additionally, the difference between these two points is more obvious with greater Reynolds numbers. Fin efficiency and fin effectiveness were calculated to assess louver performance. The air-side performance of the heat exchanger is evaluated by calculating the Colburn j
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factor and the Fanning friction f factor. The results demonstrate that adding dimples on the louver surface increases the j factor and the f factor. Likewise, adding perforation to the dimples results in the same increase. The present results indicate that compared with the in-
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performance.
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line arrangement, the staggered arrangement could effectively enhance the heat transfer
Keywords: Multilouvered fin, Dimple, Perforation, In-line, Staggered
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1. Introduction Compact heat exchangers have many industrial uses, such as in refrigeration, air conditioning, and automotive applications, and many attempts have been made to improve their performance. The commonly applicable way to improve the overall performance of the
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compact heat exchanger is to use interrupted surfaces on the fin side. The implementation of dimples, louvers, and perforation on fins has been shown to achieve the best enhancement of compact heat exchanger performance. Many numerical and experimental attempts have been
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performed to improve the heat transfer of compact heat exchangers using dimples and multilouvered fins. Kays and London [1] published the first reliable data on louvered fin surfaces.
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Beauvias [2] performed flow visualization experiments on a louvered fin array as the first study in this area. This work showed that louvers actually redirect the flow between the fins. Davenport [3] demonstrated two asymptotic flow regimes: duct directed flow and louver
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directed flow. Smoke trace studies were also performed on a scale model, which was ten times smaller, of a non-standard variant of a corrugated louvered fin geometry. Finally, he developed the heat transfer and friction correlations for corrugated louvered fin geometry.
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Chang and Wang [4] tested 27 samples of louvered fin heat exchangers with different geometrical parameters in an induced-draft, open wind tunnel and carried out extensive
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experiments on the heat transfer and the pressure drop characteristics of brazed aluminum heat exchangers. Rugh et al. [5] experimentally studied the use of a high fin density louvered surface in automobiles.
Some other attempts have been made to develop two-dimensional models of louvered fin surfaces. Achaichia and Cowell [6] modeled only one louver in a fully developed flow region by assuming cyclic boundary conditions. Suga et al. [7] performed a finite difference analysis on the two-dimensional flow and the heat transfer characteristics of louvered fins. Achaichia
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ACCEPTED MANUSCRIPT et al. [8] used a novel mesh structure with mesh lines running parallel to the louvers and extending over several fins. Dong et al. [9] studied the air-side heat transfer and pressure drop characteristics for 20 types of multi-louvered fin and flat tube heat exchangers. Hsieh and Jang [10] carried out a 3-D numerical analysis on the heat and fluid flow by increasing or
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decreasing the louver angle patterns.
The use of dimpled surfaces, as a type of enhanced surface, has received attention in the past decades due to their good heat transfer characteristics and low pressure drop penalties.
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Afansayev et al.[11] studied the effects of shallow dimples on flat plates on the overall heat
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transfer capacity and pressure drop. These authors reported a significant heat transfer enhancement (30- 40 %) at a low pressure drop cost. Ligrani et al. [12] experimentally investigated the flow structure in dimpled surfaces and demonstrated the existence of a flow recirculation zone in the upstream half of the dimple. Zhengyi et al. [13] observed a symmetric 3-D horseshow vortex inside a single dimple using laminar flow simulations.
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Additionally, the flow structure and the heat transfer in dimpled channels with fully turbulent regimes have been studied in the literatures [14]. Elyyan and Tafti [15] investigated the flow
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and heat transfer characteristics of dimpled multi-louvered fins. These authors reported not only significant heat transfer augmentation but also a considerable amount of friction loss
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augmentation through dimpled louvers. Additionally, their work showed that perforations on dimples have a sharp impact on heat transfer augmentation. In another numerical study [16], these same researchers introduced a novel geometry that was the result of altering the dimple shape. Greater heat transfer and fiction loss values were reported for this geometry. These researchers have also reported that the turbulence level increases due to the shear layer induced by their new geometry’s split dimples. Elyyan et al. [17] investigated the effect of the existence of dimpled fins in compact heat exchangers for heat transfer enhancement. These researcher conducted direct and large-eddy 4
ACCEPTED MANUSCRIPT simulations in a fin bank with dimples and protrusions over encompassing laminar, transitional and fully turbulent regimes. Shokuhmand and Sangtarash [18] conducted experimental and numerical studies on the heat transfer and flow efficiency of multilouvered fins. These authors reported that implementing simple and perforated dimples on the louvers
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enhance the heat transfer and flow efficiency significantly. In previous studies [19, 20], the j factor and f factor have been utilized to characterize the heat transfer and pressure drop of simple louver fin banks.
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The present study experimentally and numerically investigates the effect of fin geometry,
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which includes the simple louver, the in-line and staggered dimpled louver, and the in-line and staggered dimple-perforated louver, on the heat transfer in multilouvered heat exchangers. To the best of our knowledge, no similar attempts have been carried out using the temperature distribution of fin surface to calculate the heat transfer. The temperature distribution over the louver surface is simulated for five independent geometries. The
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computational results are compared with data obtained from experiments. The fin efficiency and fin effectiveness are introduced to evaluate the performance of the fin geometry on heat
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transfer. Finally, the j factor and f factor are computed to investigate the variation of heat
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transfer and pressure drop as function of the Reynolds number for different fin geometries.
2. Experimental
A low turbulence wind tunnel, Model No.TE.44/D Manufactured by PLINT and PARTNERS ENGINEERS LTD, was used in this research. The cross section of the measurement section is 460 x 460 mm and the length of the test section is 600 mm. The non-uniformity of the velocity distribution is negligible. The turbulence intensity is less than 0.2 for the largest Reynolds numbers in our test domain. The experiment apparatus is shown in Figure 1.
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Figure 1. Experimental apparatus (a) external view (b) internal view
The fin array geometry used in these calculations consists of an entrance and exit louver with four louvers on either side of the redirection louver. A scaled-up (ratio of 10) inclined louvered fin model of an automobile radiator was used as simple model without dimples and perforations. Additionally, four samples, including an in-line and staggered arrangement with dimples and perforated dimples, were constructed to have the same size. The five geometries that were studied in this research are listed in Table 1.
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Characteristic Simple louver Louver with simple dimple arrangement Louver with simple perforated dimple arrangement Louver with staggered dimple arrangement Louver with staggered perforated dimple arrangement
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Case 1 2 3 4 5
DeJong and Jacobi [19] presented a computational method to determine the minimum required rows of fins for flow visualization studies without losing periodic flow. This method
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is used in this research. Figure 2 shows the schematic structure of the three types of
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experimental apparatus with their geometrical parameters. For all the calculations in this
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article, the louver thickness is fixed at 1 mm. Further geometrical details are listed in Table 2.
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Figure 2. Schematic structure of the multilouvered heat exchanger (a) simple multilouvered fin array (b) an individual dimpled louver (c) perforated dimpled louver layout (d) perforated dimpled louver with staggered arrangement
Table 2. List of geometrical parameters
Case Simple Louver Dimpled Louver Perforated Louver
Fp* 10.0 mm 10.0 mm 10.0 mm
Lp* 10.0 mm 10.0 mm 10.0 mm
S1 * 8.0 mm 8.0 mm 8.0 mm
θ 30° 30° 30°
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S2 * 10.0 mm 10.0 mm 10.0 mm
S3 * 10.0 mm 10.0 mm 10.0 mm
r
d
-
-
6.0 mm 6.0 mm
2.5 mm
ACCEPTED MANUSCRIPT A temperature controller circuit was designed to maintain the temperature at 100°C to maintain a constant temperature condition at both sides of each louver. The controller will verify the temperature 20 times per second to achieve a minimum deviation from the setpoint. An energy meter was used to verify that energy that is consumed to set the temperature of
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both sides of each louver to the setpoint value. A data gathering system was designed to make online measurement of the temperature and the pressure. The temperatures from seven zones on the surface of different louvers have been measured using thermal sensors to determine the
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Reynolds numbers. The positions of the measurement zones are shown in Figure 3. All values were recorded when the temperature of the measurement zone stabilized. Additionally, the
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pressures upstream and downstream of each louver were measured to calculate the pressure
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drop.
Figure 3. Positions of the measurement zones (a) top view (b) side view
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boundary conforming coordinate system. Periodic boundary conditions are applied in the transverse direction to include the thermal wake effects between successive rows of fins. A Dirichlet boundary condition is applied velocity and temperature fields at the entrance of the
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array.
The governing equations can be recast into dimensionless forms using a characteristic length,
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the louver pitch LP*, a characteristic velocity, the fin array inlet velocity uin* and a * * temperature scale given by (T f − Tin ) , where Tf* is the average temperature of the louver
surface. No slip and no penetration conditions for the velocity field and a no temperature jump condition for temperature field are applied on the louvers surfaces. The non-
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* * dimensionalization would result in a Reynolds number defined by Re = Rein = uin Lp /ν and
Dirichlet boundary condition u in = 1 and Tin = 0 at the entrance of the array. The Prandtl
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number is fixed at 0.7 for air. Patrick and Tafti [21] suggested that LES method can be used to study low Reynolds turbulent flows in multilouvered geometries. DeJong and Jacobi [19]
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suggested that for a similar multilouvered array layout the flow is steady and laminar for low Reynolds numbers. Flow with higher Reynolds leads to larger vortices and will be converted from laminar to transitional and turbulent regimes. The dimensional heat flux on the louver surface is defined as
q '* = − k *
∂T * = h * (T f* − Tref* ) * ∂n
(1)
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reference temperature. Using the non-dimensionalized variables the above equation is expressed as
k* * ∂T (T f − Tin* ) = h* (T f* − Tin* )(1 − Tref ) * Lp ∂n
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q'* = −
(2)
The non-dimensional heat flux and Nusselt number can be define as:
Nu =
* f
h* L*p k*
* in
=−
∂T ∂n
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k (T − T ) *
(3)
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q' =
q '* L*p
∂T ∂n = (1 − Tref ) −
(4)
Tout − Tin 1 − Tin ln( ) 1 − Tout
(5)
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Tref = 1 −
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In this article Tref is calculated by the log-mean temperature equation:
For each louver, Tref is calculated using each computational input and output data. Tin and
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Tout are averaged on the upstream and downstream boundary of each louver, respectively. To assess the effectiveness of the multilouvered heat exchanger, we introduce fin efficiency and fin effectiveness. Fin efficiency is the ratio of heat transfer from the actual fin to the heat transfer of an imaginary fin of the same geometry and same conditions but with a temperature equal to that of the fin base. (T f* − Tref* ) q '* η= * = * q 'max (Tb − Tref* )
(6)
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ε=
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transferred by the fin. q* h * A finbase (Tb* − Tref* )
(7)
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where Afinbase is the base surface of the fin. The base surface of the fin is intersection of the louver and the tube wall and it is defined as louver thickness × louver width which is o.12,
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0.18, and 0.1 cm2 for entrance/end louver, redirection louver, and the inclined louvers, respectively.
In this section, we characterize the heat transfer by defining the Colburn j factor and the
j=
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pressure drop by the f (friction) factor. The Colburn j factor is defined as 2 h* Pr 3 * C p ρU
(8)
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where Cp, Pr and ρ are the constant heat capacity, Prandtl-number, and density of the air, respectively. U* is the mean velocity through the minimum flow area. h* can be defined in
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terms of the total heat transfer rate (Q*) and the logarithmic mean temperature difference LMTD.
Q* h = (∑ A fin ,i )LMTD *
(9)
and
LMTD =
∆To* − ∆Ti* ln(∆To* / ∆Ti* )
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The friction f factor is defined as: ∆P * 2 A fin ρU * 2 Ac
*
2
2
(kc + ke + k w )
n 2 ) 16
(12)
(13)
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kw = (
ρU *
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∆P = ∆Pt − *
(11)
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f =
where ∆Pt* and ∆P* are the total and frictional pressure drop through louver fin bank, Afin is the total surface of fin, and Ac is the minimum flow area. The parameter n stands for number
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of louver regions, kc and ke are the coefficients for pressure loss at the inlet and outlet of the fin bank, and kw is the influence factor of the louver regions. According to the geometry parameters of the condenser and the graph given by Kay and London [1], the kc is 0.4, 0.45,
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and 0.43 for the simple louver, dimpled louver, and perforated dimpled louver, respectively and ke is 0.2, 0.23, and 0.21 for the simple louver, dimpled louver, and perforated dimpled
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louver, respectively.
For comparison between the numerical and experimental data, the mean relative deviation (MRD) is defined as
1 MRD = N
x iexp − x icalc ∑ x exp i
(14)
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3.2. Computational details The momentum and energy equations were solved using second-order central-difference discretization. The commercial package Fluent 6.3 [22] was used to simulate the
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computational three-dimensional models. As mentioned previously, five geometries have been modeled to obtain the results for the CFD predictions. We have studied low and medium
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Reynolds number regimes (Re = 100 to 1200) using large eddy simulation (LES) methods. The inlet velocities lie in the range of 0.16 m/s to 1.92 m/s for this Reynolds number domain. Previous studies [16, 21] have explained that the LES method is more capable for complex geometrical configurations. A suitable grid of 2,151,382 points was adopted to obtain the
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most accurate results while being less time consuming for convergence. One half of the fin height has been modeled for the numerical calculations, and the results for the other half are gained by specifying a symmetric boundary condition along the middle surface of the entire
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domain. The inlet velocity upstream and the outflow velocity downstream of the louvers have been set as boundary conditions. The constant temperature boundary condition has been
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imposed on the wall at the base of the louvers. The properties of the air as the fluid and copper as the louver material have been listed in Table 3 at temperature 25°C which is the set room temperature for both experimental and simulation condition. Since, the air properties change with the temperature increases, property changes due to the temperature increase, has been taken into account in the simulation process.
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ACCEPTED MANUSCRIPT Table 3. Properties of air and copper at the room temperature (25°°C)
Specific Heat Capacity (J.kg-1.K-1) 1006.43 385
Thermal Conductivity (W.m-1. K-1) 0.024 401
Viscosity (kg.m-1.s-1) 1.789×10-5 -
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Density (kg.m-3) Air 1.225 Copper 8920
4. Simulation Accuracy Verification
To begin discussing the results of the various geometries we must first verify the accuracy of
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the model with one existing set of data. Here, we used the report by Zhang and Tafti [14] on
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simple multilouvered geometry.
Figure 4. Comparison of non-dimensional heat flux distribution
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Figure 4 presents the non-dimensional heat flux distribution through louvers based on data from Zhang and Tafti [14] and the presented model for Case 1 with Re = 1000. The data sets are observed to be approximately the same (less than 5% deviation).
5. Results and Discussion In this work, the effect of louver geometry on the heat transfer was investigated. Three typical geometries, which included simple, in-line dimple and perforated dimple louvers, were evaluated with respect to their heat transfer properties. Additionally, a staggered 15
ACCEPTED MANUSCRIPT arrangement of dimples and perforated dimples were taken into account as a new structure to enhance the performance of the heat exchanger. In contrast to previous studies [14, 18], the distribution of the temperature through louvers were not neglected. The middle row of the louvers array as selected for evaluation and comparison of the results obtained from the
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experimental and numerical study. Figure 5 shows the contour of the temperature distribution for five cases with Re = 600. As shown in Figure 5, in each louver the temperature decreases as the distance from the louver base increases. Additionally, the temperatures of the louvers
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increased in the direction of the fluid flow. This trend is consistent because the heat is transferred from the heat exchanger to the fluid, the fluid becomes warmer in the direction of
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flow, and the difference between the temperature of fluid and louvers decreases. Figure 6 shows that the implementation of perforations on the dimples removed trap zones and increased the flow efficiency. This effect increased the heat flux, which transferred more heat from the heat exchanger to fluid flow. The staggered arrangement of dimples and perforated
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banks.
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dimples makes the flow more turbulent to enhance the performance of multilouvered fin
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Figure 5. a) Temperature (K) contours on five cases in Re = 600 b) Louver boundary condition
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Figure 6. Vector velocity of fluid surrounding (a) simple dimple (b) perforated dimple in Re = 600
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The temperatures of the measured zones, which are shown in Figure 3, were determined numerically for five cases with Re = 1200 and were compared with the recorded value from
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the experimental apparatus in Figure 7. The results show that the calculated temperatures are in good agreement with the experimental values. Comparison of the measured temperature
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from five cases shows the smallest value is a staggered arrangement with a dimpled and perforated louver (Case 5). This result is because this arrangement makes the flow more turbulent, increases the heat transfer rate, and causes the temperature of louver surfaces decrease faster than other geometries.
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Figure 7. The temperature of louver surfaces
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Figure 8 plots the variation of the non-dimensional heat flow (q) on a louver-by-louver basis for the five different cases. As shown in Figure 8, the heat flow from first louver is greater than the last louver, and the value of the heat flow decreases downstream. Because the surface of louver 6 is greater than the other louvers, the heat flow increases at louver 6 and
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then continues its decreasing trend. It can be concluded by comparing Figures 8 (a) and (b) that the heat flow is increasing with Re number increase. In all five cases, the variation in the range of the heat flow for Re = 1200 was greater than for Re = 600. The heat flow was
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increased by adding dimples to the louver surfaces, and this value became greater in the case of perforated dimples. Additionally, the heat flow in the case of the staggered arrangement
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was greater than in the in-line arrangement. The addition of perforated dimples and applying a staggered arrangement increased the heat flow by up to 6.4% and 9.9% compared with the simple louver for Re numbers of 600 and 1200, respectively.
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Figure 8. Distribution of non-dimensional heat flow for (a) Re = 600 and for (b) Re = 1200
Figure 9 shows the total heat transfer energy ratio for the in-line dimple, the in-line dimpleperforation, the staggered dimple, and the staggered dimple-perforation samples compared with the simple louver case. These measurements were obtained using the energy meter from the experimental apparatus at different Reynolds numbers.
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Figure 9. Total heat transfer ratio compared with the simple louver case
Figure 9 shows that the total heat transfer for cases 2 through 5, which has been measured during the experiment, are nearly the same for low Reynolds numbers, but the heat transfer changes for higher Reynolds numbers.
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The Nusselt number variation on a louver-by-louver basis is shown in Figure 10. In Case 5, the average Nu numbers for louvers are primarily greater than the Nu numbers for the simple louver case. It can be concluded from Figure 10 that unsteady flow oscillations and vortex
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shedding in the downstream half of the array causes the mean heat transfer coefficient to be
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greater in the downstream half of the fin array; this is especially true for Case 5.
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Figure 10. Distribution of the Nusselt number for (a) Re = 600 and for (b) Re = 1200
The maximum heat transfer occurs where the maximum temperature difference exists. Therefore, the ideal heat transfer situation for louvered fins would exist if the temperature of the entire louver surface was the same as the wall temperature. Due to both the louver’s thermal resistance and the heat energy dissipated by flow, the temperature of louver surface is less than its base. Because dimples increase the heat transfer surface and heat transfer rate, the temperature difference between the middle regions of the dimpled louvers and the fluid flow become smaller. 22
ACCEPTED MANUSCRIPT The implementation of the dimples in different types increases the heat transfer surface by about 14% for cases 2 and 4 and 11.5% for cases 3 and 5. While, applying the dimples causes the increase of the heat transfer by different percentages for different cases. For instance, for Re number of 1200, the total heat transfer is 6.5%, 8.9%, 9.1%, and 9.9%
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greater than the simple louver geometry for cases 2, 3, 4, and 5, respectively. If we increase the heat transfer surface 14% more with the increase of the length of the simple louver instead of adding the dimples, the total heat transfer increases by about 4.5% which is less
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than all other cases mentioned above.
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The fin efficiency and fin effectiveness have been introduced to characterize the effect of implementing dimples and applying a staggered arrangement on the multilouvered heat exchanger performance. The fin efficiency and fin effectiveness for all cases with Re = 1200 have been shown in Figure 11. Figure 11(a) shows that the fin efficiency for Case 1 is greater than other geometries, which was expected given Eq. 6 because the average temperature of
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the louvers in this case is close to the base temperature. Likewise, the greater amount of heat transfer in Case 5 reduces the temperature of the louver surfaces and makes the fin efficiency
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Figure 11(b) shows the fin effectiveness values for Case 5 is greater compared with the other
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cases in the upstream half of the fin array and, in the downstream half of the fin array, the effectiveness value decreases. It can be concluded that the first louvers are more effective in transferring heat and the maximum amount of heat is transferred in these louvers. The fin effectiveness values for Case 1 through Case 5 when enhancing the performance of heat exchanger are 316%, 335%, 340%, 341%, and 344% for Re = 1200, respectively.
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Figure 11. (a) Fin efficiency and (b) fin effectiveness for all five cases with Re = 1200.
Heat transfer and pressure drop characteristics are presented in terms of non-dimensional
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parameters: the j factor and the f factor. Figure 12(a) shows the value of the j factor for all cases for different Reynolds numbers using logarithmic scales as well as the results of the simple louver of Xiaogang and Tafti [23]. It can be observed from Figure 12(a) that the value of the j factor decreases when the Reynolds number increases. Figure 12(a) also shows that implementing dimples lead to increasing the value of the j factor over the louvers. Furthermore, perforated dimples show better j factor values than the simple and dimpled louvers. Additionally, the staggered arrangement makes the flow more turbulent and causes
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Figure 12(b) shows the value of the f factor for the five cases with Reynolds numbers from 100 to 1200 using logarithmic scales as well as the results of the simple louver of Xiaogang and Tafti [23]. It can be observed that the f factor decreases as the Reynolds number increases for all cases. Figure 12(b) also illustrates that, for the same Reynolds number, the dimpled
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louver results in a greater f factor value. This larger f factor is obviously because of the effect
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of the larger pressure drop caused by the dimples. Additionally, as expected, the f factor for the staggered arrangement is greater than the in-line arrangement. Case 4 and Case 5 increase the f factor by 43% and 49% on average, respectively, whereas Case 2 and Case 3 increase the f factor value by 31% and 40% more than Case 1, respectively. The MRD value for cases 1 through 5 is 6.6%, 5.1%, 5.4%, 6.5%, and 6%, respectively. It can be seen from Figure 12
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According to Figures 12a and 12b, one can observe a deviation from linearity at about Re=400 which may be attributed to the transition between laminar and turbulent regimes. It is
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noteworthy that this nonlinearity occurs in lower amount of Reynolds number in dimple and perforation cases specially in case 5 which confirm dimples and perforations particularly in staggered arrangement make the flow more turbulent. Besides, it causes higher heat transfer and pressure drop rates.
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Figure 12. (a) j factor and (b) f factor for all cases with Re = 100 through 1200 using logarithmic scales.
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Factor j/f (1/3) [24] is adopted to evaluate the overall thermal hydraulic performance and the enhanced heat transfer effect of the louver region fins. The larger factor j/f (1/3) is, the better the enhanced heat transfer effect will be. Plots of j/f (1/3) factor versus Re number for different cases are presented in Figure 13. It can be seen from Figure 13 that the j/f (1/3) factor curve in the case of staggered perforated dimpled louvers (case 5) is the highest one with respect to the other types of louvers, which can be attributed to the fact that the overall thermal performance of the case 5 is greater than the other types.
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ACCEPTED MANUSCRIPT The values of j/f (1/3) factor increased by about 23%, 28%, 29%, and 40% compared with the simple louver geometry for the cases 2, 3, 4, and 5 respectively, which indicates that the modified louvers particularly staggered perforated dimpled arrangement provided higher
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performance for heat transfer with respect to the simple louver.
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Figure 13. Plots of j/f (1/3) factor versus Re number for different cases.
6. Uncertainty Analysis
Uncertainty of each experimental result is one of the most important factors which make the
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results to be more comprehensive. These uncertainties are affected by inevitable errors
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occurring in the experimental measurements which can be interpreted to the uncertainty of individual measuring instruments. Based on the uncertainty analysis method of Kline and McClintock [25], propagation of uncertainty in the final result is affected by the uncertainties of independent variables. This method is employed to estimate the uncertainties of experimental results. The maximum uncertainties of Nusselt number, j factor, and f factor are calculated and the results are shown in Table 4.
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ACCEPTED MANUSCRIPT It can be concluded from this research work that the calculated values of Nusselt number, j factor, and f factor cover a range of possible values based on the uncertainties presented in Table 4. In addition, it should be noted that all the experiments have been repeated three
Table 4. Maximum value of uncertainties for different variables
Nusselt number ±2.4
j factor ±6.3
f factor ±5.7
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Variable Maximum value of uncertainty (%)
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times in order to have a more reliable result and to be assured of the reproducibility.
7. Conclusions
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A wide range of numerical and experimental evaluations were performed for five cases: simple louver fin bank, dimpled louver fin bank with in-line and staggered arrangement and dimpled and perforated fin bank with in-line and staggered arrangement. These experiments were performed to determine of heat transfer and pressure drop characteristics. Both the
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numerical and the experimental results show that the dimple-perforation sets with staggered arrangement had the maximum heat flux, and the total heat transfer rate increased, which was especially noticeable in larger Reynolds numbers. Experimental data showed that applying
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this geometry enhanced the heat transfer rate up to 7%, 8.2%, and 9.9% with Reynolds
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numbers of 800, 1000, and 1200, respectively, compared with the simple louver geometry. The temperature distributions through the louvers body have been calculated using numerical methods for the five cases. The simulation results are compared with the experimental data and are found to be in good agreement. The effect of dimple implementation and the application of a staggered arrangement have been evaluated using two parameters: the fin efficiency and the fin effectiveness. The results showed that dimple-perforation with a staggered arrangement had the lowest fin efficiency value but the fin effectiveness of this geometry was greater than other cases. Both j factor and the f factor for the case of dimple-
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ACCEPTED MANUSCRIPT perforation with staggered arrangement are greater compared with other geometries. Moreover, Factor j/f The values of j/f
(1/3)
(1/3)
is adopted to evaluate the overall thermal hydraulic performance.
factor increased by about 23%, 28%, 29%, and 40% in average
compared with the simple louver geometry for the cases 2, 3, 4, and 5 respectively, which
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indicates that the modified louvers particularly staggered perforated dimpled arrangement
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provided higher performance for heat transfer with respect to the simple louver.
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8. Nomenclature
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T* Tb Tf Tin Tout Tref uin* U Greek Symbols ɛ ƞ θ ν ρ Superscripts * Subscripts f, fin, louver
area, (mm2) Minimum flow area, (mm2) fin surface, (mm2) base surface of the fin, specific heat capacity, (J.kg-1.K-1) hole size, (mm) friction f factor fin pitch, (mm) heat transfer coefficient, (W.m-2. K-1) Colburn j factor thermal conductivity, (W.m-1. K-1) abrupt contraction pressure loss coefficient abrupt expansion pressure loss coefficient louver regions pressure loss coefficient dimensional louver pitch (characteristic length scale), (mm) number of louver regions number of the experimental data Nusselt number frictional pressure drop, (Pa) total pressure drop, (Pa) Prandtl number non-dimensional heat flow non-dimensional heat flux total heat transfer, (W) dimple radius, (mm) Reynolds number non-dimensional entrance / exit, redirection and inclined louver dimensions temperature, (K) non-dimensional temperature of the fin base non-dimensional fin temperature non-dimensional inlet flow temperature non-dimensional outlet flow temperature non-dimensional flow reference temperature dimensional inlet velocity (characteristic velocity scale), (m.s-1) non-dimensional mean velocity through the minimum flow area
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A Ac Afin Afinbase Cp d f Fp* h* j k* kc ke kw L p* n N Nu ∆P* ∆Pt* Pr q q' Q* r Re S1, S2 , S3
fin effectiveness fin efficiency louver angle, degree kinematic viscosity, (kg.m-1.s-1) density, (kg.m-3) dimensional quantities based on fin 30
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based on inlet based on outlet based on reference value
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in out ref
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References
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[1] W. Kays, A. London, Heat transfer and flow friction characteristics of some compact heat exchanger surfaces, Trans. ASME, 72 (1950) 1075-1097. [2] F. Beauvais, An aerodynamic look at automotive radiators, SAE Technical Paper, 1965. [3] C. Davenport, Correlation for heat transfer and flow friction characteristics of louvered fin, AIChE Symposium series, 1983, pp. 19-27. [4] Y.J. Chang, C.C. Wang, Air Side Performance of Brazed Aluminum Heat Exchangers, 3 (1996) 15-28. [5] J. Rugh, J. Pearson, S. Ramadhyani, Study of a very compact heat exchanger used for passenger compartment heating in automobiles, 28th National Heat Transfer Conference and Exhibition, 1992, pp. 15-24. [6] A. Achaichia, T.A. Cowell, Heat transfer and pressure drop characteristics of flat tube and louvered plate fin surfaces, Experimental Thermal and Fluid Science, 1 (1988) 147-157. [7] K. Suga, H. Aoki, T. Shinagawa, Numerical Analysis on Two-Dimensional Flow and Heat Transfer of Louvered Fins Using Overlaid Grids, JSME Int. J. Ser. II 33 (1990) 122-127. [8] A. Achaichia, M. Heikal, Y. Sulaiman, T. Cowell, Numerical investigation of flow and friction in louvered fin arrays, in: Proc. of the Tenth International Heat Transfer Conf. 4, Brighton, 1994, pp. 333-333. [9] J. Dong, J. Chen, Z. Chen, W. Zhang, Y. Zhou, Heat transfer and pressure drop correlations for the multi-louvered fin compact heat exchangers, Energy Conversion and Management, 48 (2007) 15061515. [10] C.-T. Hsieh, J.-Y. Jang, 3-D thermal-hydraulic analysis for louver fin heat exchangers with variable louver angle, Applied Thermal Engineering, 26 (2006) 1629-1639. [11] V.N. Afanasyev, Y.P. Chudnovsky, A.I. Leontiev, P.S. Roganov, Turbulent flow friction and heat transfer characteristics for spherical cavities on a flat plate, Experimental Thermal and Fluid Science, 7 (1993) 1-8. [12] P.M. Ligrani, N.K. Burgess, S.Y. Won, Nusselt Numbers and Flow Structure on and Above a Shallow Dimpled Surface Within a Channel Including Effects of Inlet Turbulence Intensity Level, Journal of Turbomachinery, 127 (2004) 321-330. [13] W. Zhengyi, Y. Khoon Seng, K. Boo Cheong, Numerical Simulation of Laminar Channel Flow over Dimpled Surface, 16th AIAA Computational Fluid Dynamics Conference, American Institute of Aeronautics and Astronautics, 2003. [14] X. Zhang, D.K. Tafti, Classification and effects of thermal wakes on heat transfer in multilouvered fins, International Journal of Heat and Mass Transfer, 44 (2001) 2461-2473. [15] M.A. Elyyan, D.K. Tafti, Flow and Heat Transfer Characteristics of Dimpled Multilouvered Fins, 16 (2009) 43-60.. [16] M.A. Elyyan, D.K. Tafti, A novel split-dimple interrupted fin configuration for heat transfer augmentation, International Journal of Heat and Mass Transfer, 52 (2009) 1561-1572. [17] M.A. Elyyan, A. Rozati, D.K. Tafti, Investigation of dimpled fins for heat transfer enhancement in compact heat exchangers, International Journal of Heat and Mass Transfer, 51 (2008) 2950-2966. [18] H. Shokuhmand, F. Sangtarash, P. Student, The effect of dimple and perforations on Flow Efficiency and heat transfer enhancement in Multi louvered Fin banks, Life Science Journal, 10 (2013). [19] N.C. DeJong, A.M. Jacobi, Localized flow and heat transfer interactions in louvered-fin arrays, International Journal of Heat and Mass Transfer, 46 (2003) 443-455. [20] W. Li, X. Wang, Heat transfer and pressure drop correlations for compact heat exchangers with multi-region louver fins, International Journal of Heat and Mass Transfer, 53 (2010) 2955-2962. [21] W.V. Patrick, D.K. Tafti, Computations of flow structure and heat transfer in a dimpled channel at low to moderate Reynolds number, ASME 2004 Heat Transfer/Fluids Engineering Summer Conference, American Society of Mechanical Engineers, 2004, pp. 401-412. [22] FLUENT, User’s Guide, Release 6.3, Fluent Inc., Lebanon, New Hampshire.
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[23] Z. Xiaogang, D. Tafti, Effect of Fin Pitch on Flow and Heat Transfer in Multilouvered Fins, in, Air Conditioning and Refrigeration Center. College of Engineering. University of Illinois at UrbanaChampaign., 1999. [24] J.H. Kim, J.H. Yun, C.S. Lee, Heat-Transfer and Friction Characteristics for the Louver-Fin Heat Exchanger, Journal of Thermophysics and Heat Transfer, 18 (2004) 58-64. [25] S.J. Kline, F. McClintock, Describing uncertainties in single-sample experiments, Mechanical engineering, 75 (1953) 3-8.
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Table captions Table 1. List of fin geometries Table 2. List of geometrical parameters
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Table 4. Maximum value of uncertainties for different variables
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Table 3. Properties of air and copper at the room temperature (25°C)
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Figure captions Figure 1. Experimental apparatus (a) external view (b) internal view. Figure 2. Schematic structure of the multilouvered heat exchanger (a) simple multilouvered
dimpled louver with staggered arrangement.
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fin array (b) an individual dimpled louver (c) perforated dimpled louver layout (d) perforated
Figure 3. Positions of the measurement zones (a) top view (b) side view.
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Figure 4. Comparison of non-dimensional heat flux distribution.
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Figure 5. Temperature (K) contours on five cases in Re = 600 b) Louver boundary condition. Figure 6. Vector velocity of fluid surrounding (a) simple dimple (b) perforated dimple in Re = 600.
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Figure 7. The temperature of louver surfaces.
Figure 8. Distribution of non-dimensional heat flow for (a) Re = 600 and for (b) Re = 1200.
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Figure 9. Total heat transfer ratio compared with the simple louver case. Figure 10. Distribution of the Nusselt number for (a) Re = 600 and for (b) Re = 1200.
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Figure 11. (a) Fin efficiency and (b) fin effectiveness for all five cases with Re = 1200. Figure 12. (a) j factor and (b) f factor for all cases with Re = 100 through 1200 using logarithmic scales.
Figure 13. Plots of j/f (1/3) factor versus Re number for different cases.
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Highlights An inclined louvered fin bank has been investigated experimentally and numerically.
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Effect of dimples and perforations in different arrangements has been investigated.
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Temperature distribution through louvers and pressure drop have been evaluated.
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The maximum j an f factor occurs in Staggered Perforated dimple arrangement.
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Staggered perforated dimple louver shows the best thermal hydraulic performance.
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